Extending the Lattice Boltzmann Method to Non-linear Solid Mechanics
Abstract
This work outlines a Lattice Boltzmann Method (LBM) for geometrically and constitutively nonlinear solid mechanics to simulate large deformations under dynamic loading conditions. The method utilizes the moment chain approach, where the non-linear constitutive law is incorporated via a forcing term. Stress and deformation measures are expressed in the reference configuration. Finite difference schemes are employed for gradient and divergence computations, and Neumann- and Dirichlet-type boundary conditions are introduced. Numerical studies are performed to assess the proposed method and illustrate its capabilities. Benchmark tests for weakly dynamic uniaxial tension and simple shear across a range of Poisson's ratios demonstrate the feasibility of the scheme and serve as validation of the implementation. Furthermore, a dynamic test case involving the propagation of bending waves in a cantilever beam highlights the potential of the method to model complex dynamic phenomena.
Cite
@article{arxiv.2502.00920,
title = {Extending the Lattice Boltzmann Method to Non-linear Solid Mechanics},
author = {Henning Müller and Erik Faust and Alexander Schlüter and Ralf Müller},
journal= {arXiv preprint arXiv:2502.00920},
year = {2025}
}